I read through the review, finally (took me a while) and, though it mostly looked like a good review, I noticed these little quirks, which are counter to what I have learned and believed about the game. I don't really have much to discuss, but I'd like clarification on these two points:

The Review wrote: So, if one player rolls 5, 3, 3, 2 while another rolls 4, 2, 2, 2, the first player has 3 victories.

The Review wrote: What kind of dice does Sorcerer use? That is entirely up to the players and GM, so long as all the dice are the same type. Just bear in mind that, the more sides your die of choice has, the harder it is for someone with low stats to defeat someone with high stats.

1) she was wrong. Its only 1 success.

2) Sorcerer mechanics have a fairly high chance of the lower pool winning. A single lucky 10 against an opponent who rolls all 9s and 8s is good enough for victory. Contrast this with Target Number and count successes dice pools where given the same TN the odds skew much more heavily towards a bigger pool.

In other words you have to be lucky in Sorcerer for a 3 die pool to beat a 7 die pool...but not as lucky as you'd have to be in Riddle of Steel.

Smaller die sizes increase the likely hood of ties. If the high dice are tied you go to the second and then the third etc. That means when ties are involved it isn't enough for the small pool to get a single lucky die...you have to get several lucky dice. The more likely ties are the more of an advantage the larger pool has, because the more likely the smaller pool is to run out of high dice...or in the extreme...run out of dice altogether.

So smaller die sizes make "upset" rolls less likely. Larger die sizes make "upset" rolls more likely. The difference even between d10 and d6 is pretty noticeable in this regard. Ties become common place with dice pools of 8-13 dice rolling d6s.

Valamir wrote: Sorcerer mechanics have a fairly high chance of the lower pool winning.
....
In other words you have to be lucky in Sorcerer for a 3 die pool to beat a 7 die pool...but not as lucky as you'd have to be in Riddle of Steel.

So smaller die sizes make "upset" rolls less likely. Larger die sizes make "upset" rolls more likely.

Hey Rafial,

I'm not sure that is true. The only factor that controls the overall probability of success or failure in Sorcerer is the relative size of the die pools.

Tied dice are removed from the pool.

In a 3 vs 7 situation, the larger pool is 2.33 times bigger than the smaller
If the high die ties the pools become 2 vs 6 and the larger pool is 3 times bigger.
If the second high die ties the pools become 1 vs 5 and the larger pool is 5 times bigger.

Thus each time the high die ties, the odds of winning between the pools that are left increases for the larger pool.

Since smaller die sizes increases the likelyhood of ties, they increase the number of times during the game the above scenario plays out.

Ralph's original statment is true, smaller dice favor the winner. This is well documented. That said, the effect is not really very pronounced, amounting to a shift of, at most, a couple of percent. And the effect gets less and less as the dice increase in sides. d20 v d100 is less different than d6 v d10 (ties just become even more infinitesmally unimportant). You probably ought to stay away from flipping Coins, though even that wouldn't be too big a deal. To get any real distortion in the curve, you'd have to roll dice that had some result that occured more often than .5, meaning doing something silly like rolling a d6 and counting 1-5 = 0, and 6 = 1.

Basically, given Sorcerer's priorities, it's a complete non-issue. The system works just as well, overall, with any dice.

Mike

I'd have to see the numbers crunched to buy that Mike. My admittedly rough stab at it indicates that the effect...while not overwhelming, is significant enough to be noticeable to the "naked eye".

While I agree fully that the system works just as well with any dice, I am at this point convinced that players who play several sessions with d10s and then switch to d6s will experience a noticeable reduction in the number of times the smaller pool wins.

I'm all confused now. Are we talking about how often the one pool wins over the other, or the degrees of difference by which it wins?

Best,
Ron

In my case, I was talking about how often one pool wins over another. My results are based on a python program that I let run for several days (100,000 rolls if I remember correctly). If there is an effect of die size on how often one pools wins over another, it is less than the "noise" in my results, >1% over the range of d6-d20, with pool sizes ranging from 1-10 dice. The only variable I saw affect the overall odds of which pool won was the ratio of the pools.

I totally grant that the absolute size of the pools and the die type used affect the degree of difference by which one pool will win over another.

Brilliant! This is why I'm never good with these problems. I inevitably attempt to do it formulaically and can't remember the method in anything but the simplest of cases, for whatever reason I never think to do it experimentally. Does your script just dump pure winning percentages, or does it give an indication of the margin of victory averages as well?

-Tim

talex wrote: Does your script just dump pure winning percentages, or does it give an indication of the margin of victory averages as well?

Very slick. In the interest of not entirely highjacking the review thread (though we're a bit far gone at this point,) I'll drop you a private message. I'm a perl monkey, not a python guy, but I'd like to have a gander at it to see about modding it for Sorcerer. I think it'd be useful to get some probability info on the margin of winning at various die sizes.

-Tim

talex wrote: Very slick. In the interest of not entirely highjacking the review thread (though we're a bit far gone at this point,) I'll drop you a private message. I'm a perl monkey, not a python guy, but I'd like to have a gander at it to see about modding it for Sorcerer.

I've done the same experiment a couple of times using spreadsheets. And repeatedly I've found the same results.

In any case, what Rafial and I both agree on in terms of results is that the differences in outcome are so small as to be unimportant. A player isn't going to notice less than a 5% difference in frequency of success. And the differences are always less than that. We can quibble about the fine details if we like, but that's the only important conclusion to be drawn.

Even if it did make a larger difference, would it matter then? Which way makes more "sense" for Sorcerer? Disparity in pools meaning more likely success, or less likely success? I can't think of any reason why it's pertinent.

Mike

Mike you are correct. I'm baffled by how badly I misinterpreted my data when I first generated it six months ago.

I regenerated my data sets last night using the sorcerer method of discarding ties, and built the graphs into a web page for everyone's amusement.

Pool ratio is still definitely strongest overall factor in determining odds of success, but its now clear to me that die size does have an effect, which grows in step with absolute pool size. In the ranges I ran (1-12 dice), the difference in outcomes between d20 and d6 looks to be around 5%, with smaller die sizes favoring the larger pool, as originally stated on this thread. I stand corrected.

Also, larger absolute pools at the same ratio favor the larger pool by a slight margin.

Those charts ought to convince anyone (assuming they can read a chart) that the differences are unimportant.

BTW, Ralph, in Donjon, the differences are way more pronounced because of the effect of ties, so maybe that's what you're thinking of. That's a completely different game going from d20 down to d10 (or, heaven forfend, d6).

Mike

Ok, I hate to belabor this issue, but the graphs aren't really helping. They're just graphing numbers without any indication of the accuracy of the numbers generated. There are certain things about how the graphs are displayed that red flag them in my mind (note: red flag =/ they're wrong. red flag = more information please).

First the graph of 5:5 and 6:6 are exactly what I'd expect. All lines line up perfectly. The tie effect comes from changing the ratio of the pool size, so with equal pool size, there is no effect. However 3:3 and 2:2 ARE showing an effect. Since I can't think of a good mathematical reason for why the graph of 3:3 would look different from the graph of 5:5 both of which show the expected 50%, Red Flag is raised. Something is going on there I don't understand.

Second, I don't know how the number generation accounted for ties. I see a note where graphs were altered to make the data continuous, but this is erroneous. The graph cannot and should not be continuous. You have either 1 or more victories for the large pool (positive numbers) or 1 or more victories for the small pool (negative numbers). There should be a complete gap at 0 because ties do not stand. I'm not sure why this adjustment was made, but it confuses the heck out of me and raises the question as to whether the tied results are being accounted for correctly in whatever system is rolling the dice.


I went and prepared a grunt work spreadsheet where I simply listed every single possible combination of a 3 die d4 pool in the columns and ever single possible combination of a 2 die d4 pool in the rows, and then a second sheet using the same pools with d6s. I chose the small number of dice simply to keep the number of cells manageable. I suppose one could do a 8d10 vs 4d10 this way but it would be enormous.

The results were exactly what I expected them to be.

When the die size was dropped from d6 to d4 the number of times ties occured increased from 24.77% to 36.72%.

When ties occured on a d6, the smaller pool managed to win with subsequent dice 24.14% of the time.

When ties occured on a d4, the smaller pool managed to win with subsequent dice only 20.75% of the time

More ties occuring with a higher ratio of those ties going to the bigger pool is exactly what I've been saying.


As for how pronounced the effect is overall at these pool sizes it made a difference of 3.78%. Thats just going from d6 to d4.

The chance of rolling a double on 2d6 is 16.67%
The chance of rolling a double on 2d4 is 25%
That's 1.5x more likely dropping from d6 to d4

The chance of rolling a double on 2d10 is 10%
That's 1.67x more likely than rolling a double on 2d6
So I'd expect the difference to be even more pronounced going from d10 to d6s


As to whether a difference of 3-5% is significant enough to worry about. Well, that I guess resides in the eye of the beholder. Some people take their couple of % on D% very seriously, some do not.

I'f one were playing d20 and one found a sword that was +1 anytime the roll was even and +0 anytime the roll was odd (essentially +1/2) they'd prefer it over a straight sword...even though the statistical difference is only 2.5%

I'f one were playing d20 and one found a sword that was +1 anytime the roll was even and +0 anytime the roll was odd (essentially +1/2) they'd prefer it over a straight sword...even though the statistical difference is only 2.5%

Valamir wrote: They're just graphing numbers without any indication of the accuracy of the numbers generated.

First the graph of 5:5 and 6:6 are exactly what I'd expect. All lines line up perfectly. The tie effect comes from changing the ratio of the pool size, so with equal pool size, there is no effect. However 3:3 and 2:2 ARE showing an effect.

Second, I don't know how the number generation accounted for ties.

I see a note where graphs were altered to make the data continuous, but this is erroneous. The graph cannot and should not be continuous. You have either 1 or more victories for the large pool (positive numbers) or 1 or more victories for the small pool (negative numbers). There should be a complete gap at 0 because ties do not stand.

More ties occuring with a higher ratio of those ties going to the bigger pool is exactly what I've been saying.

For reference's sake, all of the above posts were split from the New Sorcerer review thread.

Best,
Ron

I'm a new poster here, so howdy all :)

I've written and run a script similar to the ones described earlier in this thread, but the results are quite different. I'm seeing a marked advantage for the lower score when rolled with larger dice: for example, a pool of 3 versus a pool of 6 wins 18.8% of the time with d4, but 31.5% of the time with d20

I checked some of the simpler dice combinations (e.g 1 vs 2 for d2 and d20) against the theoretical probability, with results within a couple of percentage points of what the experiment turned up. I have reasonable confidence in these numbers.

You can find the results of the script here:
http://www.highenergymagic.org/sorcdice.txt

and the script itself here:
http://www.highenergymagic.org/sorcdice.py

If the effect of die face count is as strong as this indicates, perhaps some information about how they affect play should go into the FAQ and/or later editions of the game.

The book DOES say that the # of sides on the die makes a difference, and that the larger dice favor the underdog. I'm not sure if any more statistics are really needed (though they're nice to see).

Djarb: Did you just roll a # of times, randomly? And was it true-random (like with hexbits) or was it pseudo-random? Or did you take every single possible roll in every case, and compare them that way? To do it "right" (so to speak) I think you'd have to do the latter.

Or, I'm sure someone with more probability math knowledge than myself can figure out some sort of equation.

Lxndr wrote: The book DOES say that the # of sides on the die makes a difference, and that the larger dice favor the underdog. I'm not sure if any more statistics are really needed (though they're nice to see).

Lxndr wrote:
Djarb: Did you just roll a # of times, randomly? And was it true-random (like with hexbits) or was it pseudo-random? Or did you take every single possible roll in every case, and compare them that way? To do it "right" (so to speak) I think you'd have to do the latter.

Or, I'm sure someone with more probability math knowledge than myself can figure out some sort of equation.